A local radial basis function collocation method for band structure computation of 3D phononic crystals

H Zheng, Ch Zhang, James Yang

    Research output: Contribution to journalArticlepeer-review

    22 Citations (Scopus)
    97 Downloads (Pure)


    In this paper, we further extend the local radial basis function collocation method (LRBFCM) for efficient computation of band structures of phononic crystals from 2D to 3D. The proposed LRBFCM uses one fictitious node to tackle instability problems caused by calculation of derivatives of the wave pressure. A few examples of sound pressure wave propagation are modelled to validate the developed method. Comparisons with finite element modeling demonstrate the high stability and efficiency of the new method in computation of band structures of 3D phononic crystals.

    Original languageEnglish
    Pages (from-to)1954-1964
    Number of pages11
    JournalApplied Mathematical Modelling
    Early online date11 Sept 2019
    Publication statusPublished - 1 Jan 2020

    Bibliographical note

    NOTICE: this is the author’s version of a work that was accepted for publication in Applied Mathematical Modelling. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Mathematical Modelling, 77, (2020) DOI: 10.1016/j.apm.2019.09.006

    © 2020, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/


    • Band structures
    • Eigenvalue problems
    • Interface conditions
    • Phononic crystals
    • Radial basis functions
    • Wave propagation

    ASJC Scopus subject areas

    • Modelling and Simulation
    • Applied Mathematics


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